Converting Seconds to MPH

Date: 07/11/2000 at 19:54:16
From: Bob
Subject: Seconds to MPH conversion CHART
I'm looking for a chart that converts seconds traveled to miles per
hour. I saw something in an FAQ about dividing by 3600. Thanks.

Date: 07/12/2000 at 12:07:54
From: Doctor Rick
Subject: Re: Seconds to MPH conversion CHART
Hi, Bob.
Could you specify the problem more carefully? You can't compute a
speed (miles per hour) from a time (seconds) alone. Do you want,
perhaps, times in seconds across the top and distances in feet down
the side? Then the (average) speed is the distance divided by the
time, and we need to convert feet to miles and seconds to hours. The
division by 3600 converts seconds to hours; we similarly need to
divide the distance in feet by 5280 to get the distance in miles. The
whole formula for the problem as I stated it is
D = distance in feet
T = time in seconds
S = speed in miles per hour
S = (D/5280)/(T/3600)
= (D/T)*(3600/5280)
= (15/22)D/T
You can use this formula in a spreadsheet to generate a table with the
ranges of times and distances of interest to you. For instance, in
Excel, a formula like
=15/22*$B3/C$2
can be used to generate a table like
1 2 3 4 5 6 7
-------------------------------------------------------------
1 0.682 0.341 0.227 0.170 0.136 0.114 0.097
2 1.364 0.682 0.455 0.341 0.273 0.227 0.195
3 2.045 1.023 0.682 0.511 0.409 0.341 0.292
4 2.727 1.364 0.909 0.682 0.545 0.455 0.390
5 3.409 1.705 1.136 0.852 0.682 0.568 0.487
6 4.091 2.045 1.364 1.023 0.818 0.682 0.584
7 4.773 2.386 1.591 1.193 0.955 0.795 0.682
8 5.455 2.727 1.818 1.364 1.091 0.909 0.779
9 6.136 3.068 2.045 1.534 1.227 1.023 0.877
10 6.818 3.409 2.273 1.705 1.364 1.136 0.974
11 7.500 3.750 2.500 1.875 1.500 1.250 1.071
12 8.182 4.091 2.727 2.045 1.636 1.364 1.169
13 8.864 4.432 2.955 2.216 1.773 1.477 1.266
14 9.545 4.773 3.182 2.386 1.909 1.591 1.364
15 10.227 5.114 3.409 2.557 2.045 1.705 1.461
16 10.909 5.455 3.636 2.727 2.182 1.818 1.558
where the numbers across the top are seconds and the numbers at the
left are feet. Going 11 feet in 3 seconds comes out to 2.5 miles per
hour.
- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/

Date: 07/12/2000 at 12:16:22
From: Doctor Twe
Subject: Re: seconds to MPH conversion CHART
Hi Bob! Thanks for writing to Dr. Math!
Unfortunately, seconds measures time and mph measures speed, so unless
we have more information (a fixed distance traveled, for example) we
can't convert seconds to mph. To convert seconds to hours, we divide
by 3600 - that's where that number comes in.
Let's say, for example, that we were measuring sprinters' times in the
100-yard dash and wanted to convert them to mph. We now have a fixed
distance (100 yards), so we can calculate the speed. Let's say the
sprinters ran it in 4.4 s, 4.6 s, 4.85 s and 5.2 s.
s = d / t
where: s = speed
d = distance
t = time
So for the first sprinter, we have:
s1 = 100 yd / 4.4 s
= 22.73 yd/s
Yards per second? Let's convert that to miles per hour. We can
convert yards to miles by dividing by 1760 and, as mentioned above, we
can convert seconds to hours by dividing by 3600. So we have:
s1 = (100 yd / 1760 yd/mi) / (4.4 s / 3600 s/hr)
= 0.0568 mi / 0.00122 hr
= 46.49 mph
Converting each measurement to miles and hours takes extra time. If we
have more of the same calculations to do, we can incorporate the
constants 1760 and 3600 (and even the 100 yds, if it doesn't change)
directly into the formula with a little algebra:
100 yd
----------
1760 yd/mi
s = ----------------
t
---------
3600 s/hr
100 yd 3600 s/hr
= ---------- * ---------
1760 yd/mi t
360000 mi
= ---------
1760*t hr
s = 204.54/t mph [or s = 2250/(11*t) mph for more accuracy.]
Using this "condensed" formula, we can quickly convert the other
sprinters' times into speeds:
s2 = 204.54 / 4.6
= 44.47 mph
s3 = 204.54 / 4.85
= 42.17 mph
s4 = 204.54 / 5.2
= 39.34 mph
I hope this helps! If you have any more questions, write back!
- Doctor TWE, The Math Forum
http://mathforum.org/dr.math/

Date: 07/12/2000 at 15:33:50
From: Bob Hubert
Subject: Re: seconds to MPH conversion CHART
Thanks for the answer you provided. I think my question has
complicated the issue. Let me be more specific and you tell me which
formula is best. I thought it would be very simple to locate a chart
in which the math has already been computed.
If you travel 1 mile in 60 seconds, you are traveling 60 miles per
hour. If you travel that mile in 55 seconds, what is your speed in
MPH?
I want a chart that people can carry in their cars so they do not
depend upon their unreliable automobile speedometers. They can use
a watch to time how many seconds it takes to travel from one milepost
to another, then look at this chart to correctly determine their
speed. I'm playing with the numbers and 3600 keeps coming into the
equation. I'm so close but it is driving me a little nuts that I can't
solve this.
Thanks.